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Mathematical Shortcuts and Tricks, Methods of Checking Arithmetic

MATHEMATICAL SHORTCUTS

Handy shortcuts for checking calculations, without the need of a calculator!

To check addition is correct –

  • add up the single digits of each individual number in the sum, until you are left with a single digit.
  • add these single digits together until you are, once again, left with a single digit.
  • do the same with the total these figures should be the same
EXAMPLE:

7745 + 3289  = 11034

7+7+4+5       =  23
2+3 = 5

3+2+8+9       =  22
2+2 = 4

  9

1+1+0+3+4   =    9

To check subtraction is correct:-

  • add together the total and the number you subtracted and this should equal the number you started with.

 

EXAMPLE:

4320 – 1978 = 2342

1978+2342   = 4320

To check multiplication is correct:-

  • divide the answer by one of the numbers being multiplied.
EXAMPLE:

27  x 19 =  513

513 ÷ 19 =    27

To check division is correct:-

  • multiply the answer by the number you originally divided by and this answer should be the same as the original number being divided.
EXAMPLE:

798 ÷ 14   =    57

57 x 14   =
798

HANDY HINTS

If two columns of figures should balance but don’t, subtract one total from the other and if the difference is 1, 10, 100, 9 or 99 you have probably made an error in addition.

If the difference is divisible by 9 you have probably transposed a figure (e.g.  written 89 instead of 98).

This was also sent in by KB who gave the following illustration –

If your balance says 45.25 but your statement says 42.55 – the difference is 2.70 which is divisible by 9 so, therefore, it is probably a transposed figure.  You can see the 5 and 2 have been transposed.

To “square” a number (i.e. multiply a number by itself e.g. 17 x 17)

Example A – 17 x 17

First partition the number  –  10, 7
Square the 10   (i.e. 10 x 10)
=   100
Square the 7     (i.e.    7 x 7)

=     49
Then 2 x (10 x 7)
 =   140


17 x 17 

  =  289

Example B – 52 x 52

Partition the number –  50, 2
Square the 50  (50 x 50)
 = 2,500 

(5 x 5 plus two noughts)

Square the 2    ( 2 x 2)
  = 4
Then 2 x (50 x 2)   =  200

52 x 52


  = 2,704

This shortcut was sent in by Sue Knight – thanks.

An easy way to remember your nine times table is –

a:  The figures in the answer always total 9

e.g.
2 x 9 = 18 (1+8 = 9):
7 x 9 = 63 (6+3 = 9)

b:  Deduct 1 from the number you are multiplying and the second number in the answer then becomes obvious (as it must total 9).

To multiply 8 x 9

Deduct 1 from the 8 = 7 (this is the first number of the answer)

The numbers in the answer always total 9 so the second number must be 2     

Therefore 8 x 9 =72

Now for the 11 times table –

a:  Add together the digits you are multiplying  e.g. 33 x 11 add the 3 + 3 =6

b:  Place the the answer in between the two digits  e.g. 363

Therefore 33 x 11 = 363

If the two digits add up to more than ten (e.g. 48 x 11 where 4+8=12) then you have to add the 1 to the 4 and place the 2 in the middle of the two numbers. 

Therefore 48 x 11 = 528

IF you ever need to find out the sum of all the numbers between two given digits, here is the formula :-

ADD TOGETHER THE FIRST NUMBER AND THE LAST NUMBER IN THE SEQUENCE THEN MULTIPLY BY THE NUMBER OF THE MIDDLE NUMBER IN THE SEQUENCE.

I will try to explain – say you wanted to find out the total of numbers 7 through to 35.

i.e. 7+8+9 +10+11 an so on until..33+34+35.

First add the first number in the sequence to the last number in the sequence, which in this case is –  7 + 35 = 42

Then to find the NUMBER of the middle digit in the sequence you deduct the lowest number from the highest number, add 1 then divide by 2

i.e.  35 – 7 = 28 + 1 = 29
divided by 2 =
14.5

 

NOW MULTIPLY 42 X 14.5 = 609

SO THE SUM OF ALL FIGURES BETWEEN 7 AND 35 = 609

Now all you accountants out there – give us some more (or have you forgotten them!) – contact us on june@hintsandthings.co.uk.

For more mathematical shortcuts click here.